The H.C.F. and L.C.M. of two numbers are 8 and 48 respectively. If one of the numbers is 24, then the other number is

Options

A. 48
B. 36
C. 24
D. 16

Answer

To find the other number when the H.C.F. and L.C.M. of two numbers are given, along with one of the numbers, we can use the relationship between these values.

### Step-by-Step Solution:

1. **Understand the relationship**: The relationship between the H.C.F., L.C.M., and the two numbers can be expressed as:
\[ \text{H.C.F.} \times \text{L.C.M.} = \text{Number 1} \times \text{Number 2} \]
Where:
- H.C.F. = 8
- L.C.M. = 48
- Number 1 = 24 (given)
- Number 2 = ? (to be found)

2. **Substitute the known values into the equation**:
\[ 8 \times 48 = 24 \times \text{Number 2} \]

3. **Calculate the left side**:
\[ 8 \times 48 = 384 \]
So, the equation now looks like:
\[ 384 = 24 \times \text{Number 2} \]

4. **Isolate Number 2**:
To find Number 2, divide both sides of the equation by 24:
\[ \text{Number 2} = \frac{384}{24} \]

5. **Perform the division**:
\[ \text{Number 2} = 16 \]

Thus, the other number is **16**.